How old is the car? 05 and 06 cars had a problem with excessive end float on the input shaft, which needs shimming. 07 onwards gearboxes were shimmed at the factory.
The main issue with that is the clutch pedal staying on the floor and difficulty selecting 1st and 2nd gears, but it can also cause noise problems. If your gears slot in OK and the pedal doesn't stick, your box may already be shimmed.
Is it a slight whirring noise, or really loud?
On a healthy gearbox up to temperature, there usually is a little whirring but it shouldn't be excessively loud and can only be heard inside the car, with AC off, windows up etc. That's all fine and normal. What isn't normal is excessive clattering/whirring that can be easily heard over the engine running - that's why I asked about the SMF as they create a lot of noise.
Lastly - engine mounts. Are they OEM or uprated? Some aftermarket mounts can massively amplify transmission noise.